Conway's Life, seebs

[Michali]

Conway's Life is a system where every state generates a fully deterministic next state. Its a grid of cells, each with values that change value depending upon the value of the cells adjacent to it. Sometimes stabilization occurs from an initial state, and sometimes it will never occur and the entire system (I'm guessing, will either oscillate or never repeat a prior state... not sure.) Because information can be lost, we cannot determine all past states from any usual future or end state.

When seebs mentioned this to me as a way to show how systems do not always exhibit retraceability since not all systems retain all their information, I realized something must be missing. The universe is meant to incorporate literally everything, and once again, I thought there might be lost factors going into play with these systems. I blamed it on the fact that what we were watching was the result of rules that the universe would ultimately causally play out, and that the system was dependant on them. When this was confusing, I spoke about an intuition I had regarding that there didn't seem to be a good reflection of "time" going on in this system, and I think I'm able to elaborate on what I mean now:

If its a rule, lets say:

((there is a grid of nine cells and a blue cell in the middle of (and surrounded by) grey cells will result in it turning grey))

Then I believe that we are inclined to believe that the first generation of the grid has one blue cell, and the second has no blue cells. I disagree, here, and I believe that because there is no possible way to interfere with this system (there is only 9 cells in the grid)...

there is no such thing as a blue cell in the center even though we can watch the generations on a simulation show a blue cell. In terms of the system (I know I need to better explain this) the apprent blue cell is actually a grey cell.

This is like:

-3+6-3=0=3x-4+12

This is just a complicated, but valid, way of signifying 0. Therefore, causality is not being shown here generation to generation, because there is really only one generation in Conway's life. The input state is the output state just like 3+-3 is 0.

[Farren]

That doesn't really make sense.

The state of the grid in Conway's game of life is not an arbitrary scalar derivative of its parts.

[Michali]

Originally Posted by Farren

That doesn't really make sense.

The state of the grid in Conway's game of life is not an arbitrary scalar derivative of its parts.

I am interested in what your saying, but can you explain what you mean?

[Farren]

Originally Posted by Michali

I am interested in what your saying, but can you explain what you mean?

Basically what seebs said. There are multiple states. They are not the same.

[Michali]

Originally Posted by Farren

Basically what seebs said. There are multiple states. They are not the same.

Right, but like I said. They are equivalent.

[Farren]

Originally Posted by Michali

Right, but like I said. They are equivalent.

How? Its not apparent in your original post

[seebs]

Originally Posted by Michali

Right, but like I said. They are equivalent.

No, they're not. They're different. They lead to equivalent things.

Basically, your argument seems to be this:

Part 1:
Premise: All deterministic systems are reversible.
Conclusion: Given the final state of a deterministic system, all of its prior states can be deduced.

Part 2:
Observation: In Conway's life, you cannot deduce the earlier states of a game.
Conclusion: The earlier states must not exist, because they contradict the premise.

But they do exist, and the causality and generations exist and work just fine, and it's a system which is not reversible.

We're done here. There are irreversible systems. Move on.

[seebs]

Er, no.

There are multiple states. They are distinct. We can usefully talk about these distinctions, because multiple start states could lead to a single result state. Thus, even if two states lead to the same state later, they were different previously.

Michali, the simple fact is, not everything is reversible. Trying to define the counterexamples away by claiming they aren't systems is crazy. When we say the universe "includes everything", that doesn't mean that any given single-time snapshot of it contains enough information to describe accurately all previous states.

You're begging the question something fierce, and I don't see why.

The input state is not the output state. They're different. We can show these differences in many ways, but the obvious starting point would be observing that multiple input states can yield the same output state.

[Michali]

Originally Posted by seebs

Er, no.

There are multiple states. They are distinct. We can usefully talk about these distinctions, because multiple start states could lead to a single result state. Thus, even if two states lead to the same state later, they were different previously.

Michali, the simple fact is, not everything is reversible. Trying to define the counterexamples away by claiming they aren't systems is crazy. When we say the universe "includes everything", that doesn't mean that any given single-time snapshot of it contains enough information to describe accurately all previous states.

You're begging the question something fierce, and I don't see why.

The input state is not the output state. They're different. We can show these differences in many ways, but the obvious starting point would be observing that multiple input states can yield the same output state.

Do you consider the input "state" to be a generation of the system?

-edit- also what I'm saying is all of those different input states that end up with the same end state are equal relative to the system... otherwise they aren't "states" at all. They are "states" relative to the system, because if there is no system in consideration, its just a grid of colors.

[ceptimus]

If I can show you two different start positions that lead to exactly the same final position, will that invalidate your argument?

[Michali]

Originally Posted by ceptimus

If I can show you two different start positions that lead to exactly the same final position, will that invalidate your argument?

No, see, that's the point. The suggestion your giving now was originally supposed to invalidate another argument I had, but what I'm trying to say is, those two "starting positions" are equal with respect to the system. This "Conway's Life" "system" is just a very complicated math problem, and not necessarily reflective causality. The "causal processes" we think we watch are just efficient calculations on the part of a problem solving computer or person.

The "initial state" that we plot is analogous to just randomly writting a math problem like "2X2-2+4/6"
The "end state" is analogous to whatever answer you work out "1".

This isn't causality, this is something like entailment (dealing with "if, then" conditional relationships). There is something about causality which occurs over time which is different than this. We say one thing causes another. So there are atleast two things involved in causality. This entailment relationship between states in Conways life, and mathematical problems and their solution deals with only one thing (the product of reasoning processes).

[ceptimus]

Originally Posted by ceptimus (back on page one)

If I can show you two different start positions that lead to exactly the same final position, will that invalidate your argument?

I still don't think you've answered this. If two different inputs can produce the same output, then it is nonsense to say that the initial state is defined by the final state.

[seebs]

Originally Posted by ceptimus

I still don't think you've answered this. If two different inputs can produce the same output, then it is nonsense to say that the initial state is defined by the final state.

That's why he is now absolutely committed to finding some way to claim that the initial states don't really exist, they're just illusions we see because we haven't understood the final state.

It doesn't matter that it's totally incoherent; if it's not true, his really cool argument is dead. So it must be true.

[Michali]

Originally Posted by seebs

That's why he is now absolutely committed to finding some way to claim that the initial states don't really exist, they're just illusions we see because we haven't understood the final state.

It doesn't matter that it's totally incoherent; if it's not true, his really cool argument is dead. So it must be true.

I'm actually pretty sincere in this pursuit. I seem to be very moved by your claim that (3+3) isn't identical to 6.

[seebs]

Originally Posted by Michali

I'm actually pretty sincere in this pursuit. I seem to be very moved by your claim that (3+3) isn't identical to 6.

That's not exactly my claim.

My claim is, given f(x)=x+3, that while f(3)=6, that doesn't mean that there was never a 3, and 3 is really 6.

[Iacchus]

Notwithstanding that everything has its own trajectory?

[ceptimus]

But (in Life) we could run two grids side by side. One could be full of gliders - lots of action - and then eventually settle down to a static pattern. The second grid could just be that static pattern from the start. Are you really claiming that these two 'Life universes' are equivalent?

[Michali]

Originally Posted by ceptimus

But (in Life) we could run two grids side by side. One could be full of gliders - lots of action - and then eventually settle down to a static pattern. The second grid could just be that static pattern from the start. Are you really claiming that these two 'Life universes' are equivalent?

Yes, but they are equivalent in all respects to the Conway's life system. That we can see a more complicated version of one (non stable) is dependent on the fact that we have the ability to pause and suspend the rules.

Thus a blue square in the center of grey squares simply hasn't been figured out yet to actually be a grey square. Its suspended because the interactions of a large grid have an extremely complicated total solution. But, for instance, a grid as large as the rule itself, like the (grid of 9 squares one in the middle is blue) is another way of saying what it equals, not what happens next. It only matters "what happens next" if what happens next is some sort of interference such that it is no longer surrounded by grey squares. But because the entire grid is just these nine squares, no glider or anything is going to interfere.

Essentially what it boils down to is you could right a rule for the entire initial state of the grid, and that rule would be consistent with every rule of Conway's life.

[fragment]

Thus a blue square in the center of grey squares simply hasn't been figured out yet to actually be a grey square

Why do you say it's actually a gray square? If the two states are entirely equivalent, as you argue, what grounds do you have for preferring one over the other as the actual state?

[Michali]

Originally Posted by fragment

Why do you say it's actually a gray square? If the two states are entirely equivalent, as you argue, what grounds do you have for preferring one over the other as the actual state?

Sorry I missed this. When I use the words "actually a grey square" I'm not meaning (obviously) that its actually grey in its appearance to you in color. In fact, the reason we have such a hard time conceiving this is due to the fact that I am asking you to imagine that this 3 X 3 grid, and the rules of Conway's life, are the only things that exist.

Because the state where it appeared blue is useful to us in this argument (i.e., thus blue square is functioning in our Universal system), its hard for me to say that it is "actually a grey square" when it should be described as "its actually a grey square if all there was was the 9-cell grid and the laws of Conway's life."

I am also attempting to lay out why I have an inclination to believe this, and like I said earlier, it is only "relevantly a blue square" if it has something to do with its contribution to the state at which the system stabilizes. So the reason its not actually a blue square in my example is due to the fact that the entire grid is acting under a single law. Just like when someone hallucinates and sees a pink elephant, and then they realize that they are hallucinating one, they know that their mind is reporting "there is a pink elephant in your room" but this is ultimately false. He can report the pink elephant, and be justified in saying a pink elephant is appearing in his mind, but he can't say one exists in reality. And we do say things like this... "there isn't actually a pink elephant", or "there isn't really a pink elephant". Now, I could use that pink elephant for other tasks, such as entertaining myself, or a good story for later, but it isn't real on the basis that on some important universal level it isn't relevant in the same way other things in my room are.

The difference between the use of the terms "actual cell color" and "relevant cell color" in the context of the simulator is that "actual cell color" can be used to interpret the immediate next state and "relevant cell color" is used to interpret at least two states forward. Even if we had an extremely complex initial state, it is imaginable that if you ran the system and saw how it stabilized, you could look at the initial state and "interpret the actual state" as the stabilized state. You do not have to have the individual processes to figure this out, because those processes are used due to the fact that we aren't aware of the law that dictates the initial state is (and not "will become") the stable state. Just like a grid the size of a small law, exampled before, is almost the same thing we use to describe the law.

So, someone says "Hey, how do I play Causway's life?" I say, "A blue cell by itself will become grey in the next generation". Am I giving him an experience of this 3 x 3 grid and two generations, or am I telling him how a lone blue square should be interpreted? I am inclined to think that I am telling him how it should be interpreted in the system so he can work it out.

[fragment]

Originally Posted by Michali

Sorry I missed this. When I use the words "actually a grey square" I'm not meaning (obviously) that its actually grey in its appearance to you in color. In fact, the reason we have such a hard time conceiving this is due to the fact that I am asking you to imagine that this 3 X 3 grid, and the rules of Conway's life, are the only things that exist.

Because the state where it appeared blue is useful to us in this argument (i.e., thus blue square is functioning in our Universal system), its hard for me to say that it is "actually a grey square" when it should be described as "its actually a grey square if all there was was the 9-cell grid and the laws of Conway's life."

Yes, I realise that you're arguing about what things look like from within the system, but that doesn't answer my question. I'll try restating it.

Say there is a given stable state - all grey squares. There are several hypothetical earlier states, including lone blue square, that could lead to this end state. You are saying that all of these are equivalent to the all grey square state. Fine, I'll grant that for this discussion. But that also means that the all grey squares state is equivalent to all of those other states too. Within the system I see no reason to prefer "all grey squares" to any of these other states as a way of describing the "actual" state. Rather, it appears that you've made an unsupported assumption that "grey" is a default state for a square, and that "blue" is only to be used when it is necessary. You are treating "blue" and "grey" differently without giving a reason for doing so.

[Michali]

Originally Posted by fragment

Yes, I realise that you're arguing about what things look like from within the system, but that doesn't answer my question. I'll try restating it.

Say there is a given stable state - all grey squares. There are several hypothetical earlier states, including lone blue square, that could lead to this end state. You are saying that all of these are equivalent to the all grey square state. Fine, I'll grant that for this discussion. But that also means that the all grey squares state is equivalent to all of those other states too. Within the system I see no reason to prefer "all grey squares" to any of these other states as a way of describing the "actual" state. Rather, it appears that you've made an unsupported assumption that "grey" is a default state for a square, and that "blue" is only to be used when it is necessary. You are treating "blue" and "grey" differently without giving a reason for doing so.

So, yes, very good. If you grant me all of those, then you're right in raising this question. Why shouldn't I just say that the initial state is really what the stable state is? I'm not going to argue that, and for my purposes this is fine. So long as we admit that the same could be said in reverse. Namely that, the stable state really is what the initial state is. They all mean one thing, and its this one thing that makes them equal. Its interesting to us in the latter case because we live in a system that we do not consider to be its end state. Even if you said, well the universe really is 1942, I'd be like, ok, but its also really every other state too. More importantly, its the stable state that can be reffered to with accuracy. You could say, "its really 1942 and this means Hitler is still alive", but I would say, "oh but your reffering to an unstable state where he is dead in 2008, and I believe the universe is in 2008".

Suppose some pattern explodes and in 50 generations it stabalizes at all grey cells. Now, all 49 states are equally a grey state. Except, to us, we find them incrimentally closer to a grey state based on how many more steps till we get there. Another completely different system explodes and in a different 50 generations comes to all grey cells. All of these are equal in that they are all grey states, and each is equal to the other different explosion. Even as you work this new one out, imagine 40 frames down the line you think "hey they are all grey states anyway" and you switch a frame out with the the second frame from the other explosion... you haven't changed anything at all. Your still dealing with something that will stabilize at all grey states. The only thing you've changed is how much work you'd end up doing to get there.

[fragment]

Originally Posted by Michali

The only thing you've changed is how much work you'd end up doing to get there.

Actually, by allowing states that end up in the same stable state to be switched at will with no effect, it seems you've eliminated all possibility of discovering, from within the system, the causal processes involved in getting from one state to another state. Without those you don't have the means of evaluating which states will lead to the same stable states.

[Joshua Adams]

You could understand it slowly, or if you understood the language that it was written in, you could understand it right away. Likewise, you could watch small local laws play out on one another for the end state, or you could calculate a law for the entire grid and the moment you run the simulator, it would show the end state. Either way, your not dealing with a necessary time component (cause and then effect) in this simulator.

How is this different than the universe? If you knew everything about the state of the universe, and all the laws of physics, then under determinism, you could extrapolate all the way to the end of time. Thus, the present "equals" the future. It's the same thing as figuring out future states of Game of Life, except that the states are more complex to describe, and the rules aren't known.

Now, determinism appears not to be true, and it's impossible in principle (not just in practice) to know everything about a system precisely, so none of this really applies. But the Game of Life works conceptually just like a deterministic universe would, despite your objections regarding "time".

[Michali]

[22:27] NeonQuill: let me lay out a few lines and then Ill say end of line
[22:27] Raven : this is also why I don't like philosophy. Too much theory, too little evidence
[22:28] NeonQuill: the blue cell is there only if it can be interefered with
[22:28] NeonQuill: it cannot be interfered with
[22:28] NeonQuill: the blue cell is not there
[22:29] NeonQuill: end of line
[22:29] NeonQuill: yet we saw it
[22:29] Raven : What do you mean by interfered with?
[22:29] NeonQuill: it was never there
[22:29] NeonQuill: i know i know
[22:29] NeonQuill: ok
[22:29] NeonQuill: for instance
[22:29] NeonQuill: I could set a glider, right next to the 9 squares with a blue in the middle on a larger grid
[22:29] NeonQuill: in the next generation
[22:29] NeonQuill: the glider and the blue square will meet
[22:30] NeonQuill: and flip out in some way
[22:30] NeonQuill: and stabilize
[22:30] NeonQuill: thats what i mean be interfere
[22:30] NeonQuill: if it can be
[22:31] NeonQuill: a part of the processes that end up in the stabilization
[22:31] NeonQuill: thus
[22:31] Raven : conway's life, as I've come to understand the rules, is that there are certain rules of the game to define whether a cell lives or dies. Whether it's blue or grey. One blue cell by itself starts alive, but dies, becoming grey, because it's alone. Right?
[22:31] NeonQuill: we have this backwards causation via means of reason
[22:31] NeonQuill: right
[22:32] NeonQuill: or function
[22:32] NeonQuill: i mean via means of function
[22:33] Raven : But you can't say it was always grey. Or that it didn't exist. Because it did. Fourth dimensionally it exists in a moment of time. And mathematically you can't say that it is equal to the end state of being dead, because there are other beginning states that could lead to the same all grey squares.
[22:33] Raven : one blue square in the center, or four blue squares, one in each corner. Both of these will lead to all grey squares the next generation
[22:34] NeonQuill: right
[22:34] NeonQuill: these are all the same
[22:34] Raven : and so you're trying to say that one blue square = grey, and that 4 blue squares = grey. And both of these are true. Bue 4 blue squares does not equal 1 blue square, even though they arrive at the same output. Attempting to make them equal would be the same as dividing by zero, which was the point of the previous exercise I showed you
[22:34] NeonQuill: in other words
[22:34] NeonQuill: it "means" all grey squares... reading
[22:35] Raven : You have to see it as a passage of time, you have to see it 4th dimensionally. It's not just grey. It's a process by which one blue square died, or four blue squares died, that came to mean all grey squares.
[22:35] Raven : Two seperate possibilities, diverging at a similar conclusion, yet starting at different sources.
[22:35] NeonQuill: yeah but heres why not
[22:36] NeonQuill: lets say processes occured such that
[22:36] NeonQuill: we take the glider scenario
[22:36] NeonQuill: and it hits the sole blue ssquare
[22:36] NeonQuill: and lets say it all cancels out after 14 generations
[22:36] NeonQuill: and theres all grey suares
[22:37] NeonQuill: well that initial generation
[22:37] NeonQuill: thats all grey squares
[22:37] NeonQuill: but
[22:37] NeonQuill: lets say that we rewrote the rules
[22:37] NeonQuill: such that instead of
[22:38] NeonQuill: "one blue square adjacent to none or only one will be grey in the next turn"
[22:38] NeonQuill: etc
[22:38] NeonQuill: we wrote it to encompass the relevant cell-pattern of the glider and the blue lone cell
[22:38] NeonQuill: we wouldnt need to see the geerneations
[22:38] NeonQuill: we would know that it means all grey